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# In the rectangular coordinate system above, the area in the shaded reg

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Math Expert
Joined: 02 Sep 2009
Posts: 58434
In the rectangular coordinate system above, the area in the shaded reg  [#permalink]

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16 Dec 2017, 01:28
00:00

Difficulty:

5% (low)

Question Stats:

88% (00:56) correct 12% (01:11) wrong based on 98 sessions

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In the rectangular coordinate system above, the area in the shaded region is

(A) 1 1/2
(B) 2
(C) 2 1/2
(D) 3
(E) 4

Attachment:

2017-12-15_1301.png [ 4.71 KiB | Viewed 1612 times ]

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Director
Joined: 24 Nov 2016
Posts: 618
Location: United States
Re: In the rectangular coordinate system above, the area in the shaded reg  [#permalink]

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16 Dec 2017, 11:36
Bunuel wrote:

In the rectangular coordinate system above, the area in the shaded region is

(A) 1 1/2
(B) 2
(C) 2 1/2
(D) 3
(E) 4

Attachment:
2017-12-15_1301.png

Am I missing something?

Area of triangle: $$\frac{base*height}{2}$$

Area of shaded region: Area of large triangle - Area of small triangle

Area of small triangle: $$\frac{(1*1)}{2}=\frac{1}{2}$$

Area of large triangle: $$\frac{2*height}{2}=height$$

Area of shaded region: $$height$$ $$- \frac{1}{2}$$
Director
Joined: 20 Jul 2017
Posts: 928
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: In the rectangular coordinate system above, the area in the shaded reg  [#permalink]

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25 May 2019, 04:24
exc4libur wrote:
Bunuel wrote:

In the rectangular coordinate system above, the area in the shaded region is

(A) 1 1/2
(B) 2
(C) 2 1/2
(D) 3
(E) 4

Attachment:
2017-12-15_1301.png

Am I missing something?

Area of triangle: $$\frac{base*height}{2}$$

Area of shaded region: Area of large triangle - Area of small triangle

Area of small triangle: $$\frac{(1*1)}{2}=\frac{1}{2}$$

Area of large triangle: $$\frac{2*height}{2}=height$$

Area of shaded region: $$height$$ $$- \frac{1}{2}$$

So, Area of shared region = Area of larger triangle - Area of smaller triangle.

Dimensions of larger triangle are base = 2 units, height = 2 units
Dimensions of smaller triangle are base = 1 unit, height = 1 unit

Area of larger triangle = 1/2*base*height = 1/2*2*2 = 2 units
Area of smaller triangle = 1/2*1*1 = 1/2 units

So, Area of shaded region = 2 - 1/2 = 3/2 or 1 1/2

Option A

Hope its clear!
Manager
Joined: 19 Feb 2019
Posts: 78
Concentration: Marketing, Statistics
Re: In the rectangular coordinate system above, the area in the shaded reg  [#permalink]

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28 Aug 2019, 08:38
Hi Dillesh4096

From where did u get that the height of the larger triangle is 2 units?
Its not given in the figure

Pls explain if i am missing some part of the calculation
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Joined: 03 Jun 2019
Posts: 1734
Location: India
Re: In the rectangular coordinate system above, the area in the shaded reg  [#permalink]

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28 Aug 2019, 09:57
Bunuel wrote:

In the rectangular coordinate system above, the area in the shaded region is

(A) 1 1/2
(B) 2
(C) 2 1/2
(D) 3
(E) 4

Attachment:
2017-12-15_1301.png

Area of shaded region = 2*2/2 - 1*1/2 = 2 - 1/2 = 1 1/2

IMO A
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Re: In the rectangular coordinate system above, the area in the shaded reg   [#permalink] 28 Aug 2019, 09:57
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